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A mass attached to a spring, set in a container of molasses (a thick liquid) acts like a damped simple harmonic oscillator. The mass is 9 kg, the spring has a spring constant of 81 N/m and the molasses provides a damping force of 54 N-s/m. (a) The system is (A) underdamped (B) overdamped (C) critically damped (b) A force of F(t) = -7e-31 (in N) is applied to the mass. If the method of undetermined coefficients is used to find a particular solution, which of the following is the best choice as a trial solution? (c) Initially, at t = Os, our mass is moving at a speed of 5 m/s as it passes through its equilibrium position (x = 0m). If we are still under the force from part (b), at what positive time, in seconds, does it again pass through x 0m? (If it never does, type dne).

A mass attached to a spring, set in a container of molasses (a thick liquid) acts like a damped simple harmonic oscillator. The mass is 9 kg, the spring has a spring constant of 81 N/m and the molasses provides a damping force of 54 N-s/m. (a) The system is (A) underdamped (B) overdamped (C) critically damped (b) A force of F(t) = -7e-31 (in N) is applied to the mass. If the method of undetermined coefficients is used to find a particular solution, which of the following is the best choice as a trial solution? (c) Initially, at t = Os, our mass is moving at a speed of 5 m/s as it passes through its equilibrium position (x = 0m). If we are still under the force from part (b), at what positive time, in seconds, does it again pass through x 0m? (If it never does, type dne).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem #9: A mass attached to a spring, set in a container of molasses (a thick liquid) acts like a damped simple harmonic oscillator. The mass is 9 kg, the spring has a spring constant of 81 N/m and the molasses provides a damping force of 54 N-s/m. (a) The system is (A) underdamped (B) overdamped (C) critically damped (b) A force of F(t) = -7e-31 (in N) is applied to the mass. If the method of undetermined coefficients is used to find a particular solution, which of the following is the best choice as a trial solution? (c) Initially, at t = Os, our mass is moving at a speed of 5 m/s as it passes through its equilibrium position (x = 0m). If we are still under the force from part (b), at what positive time, in seconds, does it again pass through x = 0m? (If it never does, type dne).
Transcribed Image Text:Problem #9: A mass attached to a spring, set in a container of molasses (a thick liquid) acts like a damped simple harmonic oscillator. The mass is 9 kg, the spring has a spring constant of 81 N/m and the molasses provides a damping force of 54 N-s/m. (a) The system is (A) underdamped (B) overdamped (C) critically damped (b) A force of F(t) = -7e-31 (in N) is applied to the mass. If the method of undetermined coefficients is used to find a particular solution, which of the following is the best choice as a trial solution? (c) Initially, at t = Os, our mass is moving at a speed of 5 m/s as it passes through its equilibrium position (x = 0m). If we are still under the force from part (b), at what positive time, in seconds, does it again pass through x = 0m? (If it never does, type dne).
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